Ply cracking and stiffness degradation in cross-ply laminates under biaxial extension, bending and thermal loading

Transverse ply cracking often leads to the loss of stiffness and reduction in thermal expansion coefficients. This paper presents the thermoelastic degradation of general cross-ply laminates, containing transverse ply cracks, subjected to biaxial extension, bending and thermal loading. The stress and displacement fields are calculated by using the state space equation method [Zhang D, Ye JQ, Sheng HY. Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos Struct [in press].]. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. After introducing the concept of the effective thermoelastic properties of a laminate, the degradations of axial elastic moduli, Poisson’s ratios, thermal expansion coefficients and flexural moduli are predicted and compared with numerical results from other methods or available test results. It is found that the theory provides good predictions of the stiffness degradation in both symmetric and antisymmetric cross-ply laminates. The predictions of stiffness reduction in nonsymmetric cross-ply laminates can be used as benchmark test for other methods.     

Crack initiation and crack propagation under thermal cyclic loading

Theoretical and experimental investigations of crack initiation and crack propagation under thermal cyclic loading are presented. For the experimental investigation a special thermal fatigue test rig has been constructed in which a small circular cylindrical specimen is heated up to a homogeneous temperature and cyclically cooled down under well defined thermal and mechanical boundary conditions by a jet of cold water. At the end of the cooling phase the specimen is reheated to the initial temperature and the following cycle begins. The experiments are performed with uncracked and mechanically precracked specimens of the German austenitic stainless steel X6CrNi 1811.

In the crack initiation part of the investigation the number of load cycles to initiate cracks under thermal cyclic load is compared to the number of load cycles to initiate cracks under uniaxial mechanical fatigue loading at the same strain range as in the cyclic thermal experiment. The development of initiated cracks under thermal cyclic load is compared with the development of cracks under uniaxial mechanical cyclic load.

In the crack propagation part of the investigation crack growth rates of semi-elliptical surface cracks under thermal cyclic loading are determined and compared to suitable mechanical fatigue tests made on compact-tension and four-point bending specimens with semi-elliptical surface cracks. The effect of environment, frequency, load shape and temperature on the crack growth rate is determined for the material in mechanical fatigue tests.

The theoretical investigations are based on the temperature distribution in the specimen, which is calculated using finite element programs and compared to experimental results. From the temperature distribution, elastic and elastic-plastic stress distributions are determined taking into account the temperature dependence of the material properties. The prediction of crack propagation relies on linear-elastic fracture mechanics. Stress intensity factors are calculated with the weight function method and crack propagation is determined using the Paris relation.

To demonstrate the quality of the crack growth analysis the experimental results are compared to the prediction of crack propagation under thermal cyclic load.     

Mesh‐independent matrix cracking and delamination modeling in laminated composites

The initiation and evolution of transverse matrix cracks and delaminations are predicted within a mesh‐independent cracking (MIC) framework. MIC is a regularized extended finite element method (x‐FEM) that allows the insertion of cracks in directions that are independent of the mesh orientation. The Heaviside step function that is typically used to introduce a displacement discontinuity across a crack surface is replaced by a continuous function approximated by using the original displacement shape functions. Such regularization allows the preservation of the Gaussian integration schema regardless of the enrichment required to model cracking in an arbitrary direction. The interaction between plies is anchored on the integration point distribution, which remains constant through the entire simulation. Initiation and propagation of delaminations between plies as well as intra‐ply MIC opening is implemented by using a mixed‐mode cohesive formulation in a fully three‐dimensional model that includes residual thermal stresses. The validity of the proposed methodology was tested against a variety of problems ranging from simple evolution of delamination from existing transverse cracks to strength predictions of complex laminates withouttextita priori knowledge of damage location or initiation. Good agreement with conventional numerical solutions and/or experimental data was observed in all the problems considered. Published 2011. This article is a US Government work and is in the public domain in the USA.     

Interlaminar shear stresses in laminated composite plates under thermal and mechanical loading

The combined effects of thermal and mechanical loadings on the distribution of interlaminar shear stresses in composite laminated thin and moderately thick composite plates are investigated numerically using the commercially available software package MSC NASTRAN/PATRAN. The validity of the present finite element analysis is demonstrated by comparing the interlaminar shear stresses evaluated using the experimental measurement. Various parametric studies are also performed to investigate the effect of stacking sequences, length to thickness ratio, and boundary conditions on the interlaminar shear stresses with identical mechanical and thermal loadings. It is observed that the effect of thermal environment on the interlaminar shear stresses in carbon-epoxy fiber-reinforced composite laminated plates are much higher in asymmetric cross-ply laminate and anti-symmetric laminate compared to symmetric cross-ply laminate and unidirectional laminate under identical loadings and boundary conditions.     

Numerical investigation of matrix cracking propagation in cross‐ply laminated composites subjected to three‐point bending load using concurrent multiscale model

The purpose of the present study is to analyze fiber‐matrix debonding and induced matrix cracking formation as two major micromechanical damage modes in cross‐ply composite laminates using a two‐dimensional numerical approach. To this aim, the cross‐ply laminates containing 90‐degree layers are modeled, where the fibers are arranged randomly in transverse plies. Damage modes in this numerical model are simulated by the cohesive surface method. The performed analyses reveal that in the laminates with 90‐degree layers located in the outer positions, the primary micro damage mode is micro matrix cracking which is initiated from the fiber‐matrix debonding damage mode and will be followed by matrix cracking. The main benefit of the present study in comparison to other numerical methods is proposing a virtual test method for damage analysis of different cross‐ply laminates in which, the matrix cracking formation will emerge physically in a random and antisymmetric pattern similar to the experimental observations.     

Interface damage of SiC/Ti metal matrix composites subjected to combined thermal and axial shear loading

A three-dimensional micromechanical finite element model is developed to study initiation and propagation of interface damage of unidirectional SiC/Ti metal matrix composites (MMCs) subjected to combined thermal and axial shear loading. Effects of various important parameters such as manufacturing process thermal residual stress, fiber coating and interface bonding are investigated. The model includes a representative volume element consists of a quarter of SiC (SCS-6) fibers covered by interface and coating, which are all surrounded by Ti-15-3 matrix. Appropriate boundary conditions are introduced to include effects of combined thermal and axial shear loading on the RVE. A suitable failure criterion for interface damage is introduced to predict initiation and propagation of interface de-bonding during shear loading. It is shown that while predictions based on perfectly bonded and fully de-bonded interface are far from reality, the predicted stress–strain curve for damaged interface demonstrates very good agreement with experimental data.     

An interaction energy integral method for T-stress evaluation in nonhomogeneous materials under thermal loading

An interaction energy integral method is developed for the finite element evaluation of the T-stress in nonhomogeneous materials under thermal loading. A domain-independent integral expression for extracting the T-stress is proposed for nonhomogeneous materials even when the integral domain intersects the interface. Then it is set in the extended finite element method (XFEM) so that the T-stress can be solved with high accuracy and efficiency. Several representative examples are solved to show the validity and the domain-independence of the method. A crack problem in a functionally graded thermal barrier coating (TBC) is also analyzed. Finally, the influences of material continuity on the T-stress are investigated. It can be found that the discontinuity of both thermal expansion coefficient and Young’s modulus affects the T-stress dramatically.     

A penny-shaped crack in a functionally graded piezoelectric strip under thermal loading

The mixed-mode thermoelectromechanical fracture problem for a functionally graded piezoelectric material (FGPM) strip with a penny-shaped crack is considered. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under thermal loading. The crack faces are supposed to be insulated thermally and electrically. The thermal and electromechanical problems are reduced to singular integral equations and solved numerically. The stress and electric displacement intensity factors are presented for different crack size, crack position and material nonhomogeneity.     

Interlaminar stresses in thick rectangular laminated plates with arbitrary laminations and boundary conditions under transverse loads

In the present study, interlaminar stresses resulting from bending of thick rectangular laminated plates with arbitrary laminations and boundary conditions are analyzed analytically based on a three-dimensional multi-term extended Kantorovich method (3DMTEKM). Using the principle of minimum total potential energy, three systems of coupled ordinary differential equations with non-homogeneous boundary conditions are obtained. Then an iterative procedure is established to achieve analytical solution. The results obtained from this theory are compared with those of analytical solutions existing in the literature. It is found that the present results have excellent agreements with those obtained by layerwise theory. The results show that the multi-term EKM converges within only three terms of trial functions and the single-term EKM is not able to estimate the local interlaminar stresses near the boundaries of laminates. Finally, the power of the present approach in obtaining the interlaminar stresses in thick rectangular laminated plates with general types of boundary conditions and lay-ups is examined.     

Variational approach development in analysis of matrix cracking and induced delamination of cross-ply composite laminates subjected to in-plane shear loading

Matrix microcracking and induced delamination propagating from the edge of microcracks in cross-ply composite laminates with [0_n/90_m]_s and [90_m/0_n]_s layups under in-plane static shear loading are investigated. An admissible stress field, which satisfies all of equilibrium equations, boundary conditions, and continuity of interfaces, is approximated. Then using the principle of the minimum complementary energy, the stress state is obtained from calculations of variation. The calculated stress state gives the stiffness reduction and the total strain energy of the laminated composite structure. Finally, the strain energy release rate of a general cross-ply laminate due to initiation and propagation of matrix cracking and induced delamination can be deduced. Results of the developed approach are in good agreement with experimental observations and finite element analyses, which confirms its accuracy.     

Transverse cracking and delamination in cross-ply gr/ep composites under dry, saturated and immersed fatigue

Motivated by experimental observations, the finite element method is employed to model the competition between the transverse cracking and delamination modes of failure that occur in cross-ply AS4/3501-6 gr/ep coupons subjected to fatigue. The results explain the extensive delaminations and reduced crack densities that arise under immersed fatigue, as compared with fatigue in air. This revised version was published online in August 2006 with corrections to the Cover Date.     

Matrix cracking and delamination in laminated composites. Part I: Ply constitutive law, first ply failure and onset of delamination

Matrix cracking and delamination are the main initial forms of damage in advanced laminated composites manufactured by stacking unidirectional plies of fiber reinforced polymers. In this paper, the onset of matrix cracking is determined for in-plane stress states; in addition, delamination promoted by matrix cracks is analyzed. Taking into account that under in-plane shear stresses composite laminates show a non-linear response prior to the formation of a macro-crack, a plastic-damage model is proposed and implemented. The models predictions correlate well with published experimental data.     

Damage mechanisms and failure modes in cross-ply laminates under monotonic tensile loading: The influence of fiber sizing

In this study, the effect of fiber-matrix interphase on the damage modes and failure mechanisms in (0, 90₃), cross-ply graphite-toughened epoxy laminates is investigated. Two material systems (designated as 810 A and 810 O) with the same fiber and same matrix, but with different fiber sizings, were used to study the effect of the interphase. The system designated as 810 A contained an unreacted Bisphenol-A (epoxy) sizing, while a thermoplastic polyvinylpyrrolidone (PVP) sizing was used in the 810 O system. Damage accumulation in the cross-ply laminates under monotonic tensile loading was monitored using edge replication, x-ray radiography, acoustic emission, optical and scanning electron microscopy. Results indicate that the fiber-matrix bond strength is lower in the 810 O system compared to the 810 A system. Transverse matrix cracking initiates at a significantly lower stress level in the 810 O laminate. The 810 O laminates also exhibit longitudinal splitting, while the stronger bonding suppress this damage mode in the 810 A laminates. Numerous local delamination occur on the 0/90 interface at the intersection of 0 and 90 degree ply cracks, in the 810 O laminates. These are absent in the 810 A laminates. The failure modes are also different in the two material systems used in this study. The 810 A laminate exhibits a brittle failure, controlled by the local stress concentration effects near broken fibers. In the 810 O laminates, the presence of longitudinal splits result in the reduction of stress concentration effects near fibe fractures. This results in a global strain controlled failure in the 810 O system. It is concluded that the presence of different fiber sizings result in different damage modes and failure mechanisms in the cross-ply laminates used in this study.Research Associate, Research Assistant, Alexander Giacco Professor and Professor respectively.     

Analysis of multi-layered filament-wound composite pipes under combined internal pressure and thermomechanical loading with thermal variations

The composite pipes manufactured by filament winding technology have anisotropic behavior owing to different reinforced ply angles. Composite pipes can be exposed to the thermomechanical loading due to hot fluid that flows into them. In this paper, based on the three-dimensional anisotropic elasticity, an exact elastic solution for thermal stresses and deformations of the pipes under internal pressure and a temperature gradient has been studied. Giving heat convection conditions the variation of temperature field within the pipe is obtained by solving the conduction equation at the wall. The influence of temperature field in the governing equations of thermoelasticity has been considered via a constitutive law. The shear extension coupling is also considered because of lay-up angles. Stress, strain and deformation distributions for different angle-ply pipe designs are investigated using the present theory.     

Analysis and simulation of cracking patterns in coating under biaxial tensile or thermal stress using analysis/FEM strain-accommodation method

The cracking patterns in coatings under biaxial tensile or thermal stress are analyzed by the “analysis/FEM strain-accommodation method” that combines the strain of the substrate with a coating obtained from thermo-elastic analysis with the strain of the substrate calculated by a finite element method. The simulation using this method is effective not only for expressing the cracking patterns observed in punch press tests of disk specimens with WC-Co cermet and Al₂O₃-TiO₂ ceramic coatings but also predicting the cracking process for the coating deposited on a part with a complex shape under thermal stress.     

Constituent damage mechanisms in metal matrix composites under fatigue loading, and their effects on fatigue life

Load controlled fatigue experiments were performed on 8-ply unidirectional ([0]₈) SCS-6-Ti-15-3 metal matrix composites (MMCs) at different temperatures, and the results were interpreted in terms of the overall three-regime framework of fatigue. The emphasis was on understanding the mechanisms and mechanics of constituent damage evolution, and their effects on fatigue life. Most tests were performed at an R-ratio of 0.1, but limited fully-reversed (R = −1) tests were conducted. In regime 1, damage was fiber failure dominated, but the exact mechanisms were different at room and elevated temperatures. In regime 2, observation of matrix cracks and persistent slip bands provided convincing evidence of matrix dominated damage. Weak fiber-matrix interfaces contributed to crack bridging. However, fiber fracture also played an important role in regime 2; tension-tension and tension-compression tests showed similar lives on a maximum fiber stress basis, although the strain range, which primarily controls matrix crack growth, was almost double for R = −1 compared with R = 0 or 0.1. Good agreement was obtained from the different R-ratio tests, between the MMC and matrix data, and data at room and elevated temperatures, when compared based on the strain range in the tension part of a cycle. Analyses and observations of fiber pull-out lengths and fiber fractures in the matrix crack wake provided evidence of fiber damage; the analyses also helped to explain increased fiber bridging with fiber volume fraction. Issues of fatigue life prediction are briefly discussed.     

Interface diffusion-induced creep and stress relaxation in unidirectional metal matrix composites under biaxial loading

Analytical solutions are developed for interface diffusion-induced creep and stress relaxation in unidirectional metal matrix composites under biaxial transverse loading. The driving force for the interface diffusion is the normal stress acting on the interface, which is obtained from rigorous Eshelby inclusion theory. The solutions are a function of the applied stress, volume fraction and radius of the reinforced-fiber, the modulus ratio between the fiber and the matrix, specially, exhibit a strong dependence of creep rate and stress relaxation behavior on the biaxial stress ratio. Moreover, the solution for the interface stress presented in this study also gives some insight into the relationship between the interface diffusion and interface slip. For the application of the solutions in the realistic composites, the scale effect is taken into account by detailed finite element analysis based on a unit cell model.     

力、热载荷作用下纤维在复合材料中的界面应力传递行为

采用三维光弹性实验应力分析和有限元计算两种方法,在拉拔载荷和热残余应力联合作用下,对单丝拔出树脂基复合材料三维冻结切片界面剪应力进行了研究。实验结果和计算表明,在单纤维与基体界面的埋入端及埋入末端附近出现界面残余剪应力的极值;力、热载荷作用下纤维界面剪应力呈抛物线分布,单丝埋入端附近是应力的主要传递区域,最先达到危险应力,出现界面脱胶破坏,然后剪应力沿纤维埋入长度由纤维埋入端附近向埋入末端逐渐传递;界面热残余应力对界面剪应力的影响是使纤维埋入末端应力集中程度降低,使界面剪应力最大值增大。      

A solution method for frictional contact problems of a crack in FGMs under mechanical and thermal loads

This article provides a numerical treatment of a finite crack in an interfacial layer with spatially varying elastic properties under in-plane mechanical and thermal loading conditions. The variation of stress intensity factors and energy release rates with the functions which are governing the material properties of the interfacial layer is studied. Transient and steady-state response of a central crack in FGMs subjected to the mechanical and thermal loads are investigated. Unlike earlier studies which consider the cracks encountered as open, the current investigation studies cracks in an essentially compressive environment in which the crack faces are in contact and frictional effects play an important role. To solve this contact problem, a simple and efficient, iterative finite element method developed by authors is used. Numerical examples are provided to verify the technique and the results are compared with those of the published papers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermal mismatch induced disorder of beta-eucryptite and its effect on thermal expansion of beta-eucryptite/Al composites

In this paper, beta-eucryptite/Al composites with different volume fraction of beta-eucryptite particles (Euc/Al) were prepared by spark plasma sintering process. The microstructures of the composites were studied by transmission electron microscope. The phase compositions and thermal physical properties of the composites were analyzed by X-ray diffraction and thermal dilatometer. The change of peaks intensity ratio of beta-eucryptite (2 0 0) to beta-eucryptite (2 0 2) plane after 12 months of aging in room condition and at elevated temperature (40–300 °C) was used to characterize the disorder of beta-eucryptite, which was due to the high thermal mismatch stress in the composite. The results indicate that the disorder of beta-eucryptite can recover when the thermal mismatch stress in beta-eucryptite is released after 12 months of aging or at elevated temperature. Both compressive stress and tensile stress could induce the disorder of eucryptite (2 0 0) plane. The relationships among CTE behavior of the composite, the phase transformation of beta-eucryptite and the thermal mismatch stress were discussed.